1. Answer the questions below for the following utility fLu1ctions: - My? - + - r+1n(y:|. . r3+y3. .m. {a} Find the marginal utilities and marginal rate of substitution. [2) {b} Do preference; satisfy \"more is better\"? Explain. (1) {c} Are preferences convef? Explain. [2} 2. An individual like; to mnsume only two goods, good 1 and good 2. Let :r 2 [l and y 3 fl denote the quantities of good 1 and 2, respectively. Her preferences over bLuldles {my} are represented by the utility function May} = m+ . The price of good 113:1 = 2 and the price of good 2,193 = 5. The individual has inoome m 2 I]. [a] Draw the budget line when m = llll]. What is the slope of the budget line? (3] {b} Write down the Lagrangian function for the individual's ehoiee problem. {2] {c} Suppose {up} such that m := and y := I] solves the choice problem. Find {my} {2} {d} What is the minimum amount of income required for the solution to be such that the individual consumes positive quantities of both goods? [2] {e} Suppose m is less than the income level that you found in part {d}. Argue that the solution must be such that the individual oonsumes positive quantity of only good 2. Hint: First argue that the individual must consume positive quantity of at least one good. Second argue that it is not optimal for the individual to consume .1: :3 El and y = I}. (2) 3. Consider the utility function 2.1: + 3y. {a} Using mdiEerence tunes and budget line diagram nd the demand functions for both goods. {2] {b} Find the indirect utility,r function. (2] {c} Find the expenditure inction. [2} {d} Find the mmpensated demand functions for both goods. [2} {e} The consumer's income in = 10a. The initial price; are 331 = 1 and p2 = 1. The gmernment decides to impose a $1 per unit tax on the quantity,r :1; purchased by the consumer. What are the total effect: substitution eeet and income effect as a result of this tax? [2}